Problem: Rewrite as a simplified fraction. ${0.\overline{6} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 6.6666...\\ 1x &= 0.6666...\end{align*}}$ Subtracting the two equations, we have: ${9x = 6}$ ${x = \dfrac{6}{9}} $ ${x = \dfrac{2}{3}} $